# Math

posted by .

A 5.0 m tree is leaning 5° from the vertical. To prevent it from leaning any farther, a stake needs to be fastened 2 m from the top of the tree at an angle of 60°with the ground. How far from the base of the tree, to the nearest metre, must the stake be?

• Math -

I visualize a triangle ABC such that
AB = 3
angle B = 95°
angle C = 60° , so angle A = 180-95-60 = 25°
BC = x, our required length

By the sine law:

x/sin25 = 3/sin60
x = 3sin25/sin60 = appr 1.46 m

## Similar Questions

1. ### trig

Because of prevailing winds, a tree grew so that it was leaning 4 degrees from the vertical. At a point, 35 meters from the tree, the angle of elevation to the top of the tree is 23 degrees. Find the height h of the tree
2. ### ALGEBA

A POLE IS LEANING AGANIST A TREE SO THAT THE TOP OF THE POLE IS AT A HEIGHT OF 22FT.THE BUTTON OF THE POLE IS ON THE GEOUND 6FT AWAY THE TREE.WHAT IS THE SLOPE OF THE POLE LEANING AGAINST THEE TREE
3. ### math

Because of the prevailing winds, a tree grew so that it was leaning 6° from the vertical. At a point 100 feet away from the tree, the angle of elevation to the top of the tree is 22°55'
4. ### geometry

A tree is growing at an angle out of the ground, 15°17' from vertical. Standing 10 ft away from the base, the angle to the top of the tree is 25°17'. What is the height of the tree?
5. ### Math

An 8 meters bamboo pole is leaning against a coconut tree. The foot of the pole is 3 meters from the base of the tree. What angle does the pole make with the tree if the pole reaches up to the top of the tree?
6. ### math

From 70 feet away from the base of a tree on level ground, the angle to the top of a tree is 60⁰. What is the height of the tree?
7. ### Math

A pine tree stands 10 meters tall but due to a windstorm it is leaning at a 60 degree angle with the ground. Find an exact expression for the length of the shadow of the tree when the sun is directly overhead.
8. ### math

The trunk of a leaning tree makes an angle of 12 degrees with the vertical. To prevent the tree from falling over, a 35.0 m rope is attached to the top of the tree and is pegged into level ground some distance away. if the tree is …
9. ### trigonometric oblique triangle

you are standing 40m from the base of a tree leaning 8 degree from the vertical away from you. the angle o elevation from your feet to the top of the tree is 20 seconds and 50 minutes find the height of the tree.
10. ### Math

1) A ladder that is 15m long is leaning up against a building. The ladder makes an angle of 30 degrees with the ground. a) Find an exact expression for the height at which the top of the ladder contacts the wall of the building. 2) …

More Similar Questions